SovietRxiv · Open Access in English
Rediscovering the Soviet scientific archive, in English
25357 full-text translations 14926 English PDFs 22539 abstracts
Showing 50 of 5847 papers in Mathematics
The paper studies classical solvability of Dirichlet and Neumann boundary value problems for general second order linear elliptic operators whose coefficients may be discontinuous across an interior Lyapunov surface. It formulates transmission conditions for the jump of the solution and its conormal…
This note continues the author’s development of the method of indexials for locating subgroups of finite groups, focusing on the additional multiplier that appears in earlier existence criteria for subgroups. It introduces primary specially arithmetically closed extensions, chains of such extensions…
This paper derives a priori estimates for solutions of second order elliptic equations in finite domains, with coefficients subject to ellipticity and integrability conditions and constants independent of coefficient moduli of continuity. It extends Stampacchia’s estimates by proving endpoint and re…
This note studies regularity properties of solutions in the whole space to constant coefficient partial differential equations, using spaces of rapidly decreasing or exponentially growing functions and their duals. It refines hypoellipticity results by showing that growth restrictions on generalized…
This paper studies conditions under which functions in analytic or quasi-analytic classes on an interval can be expanded in a quasi-power series generalizing the Taylor series. It refines an earlier expandability theorem by imposing conditions on the logarithmically convex derivative bounds and the …
This paper studies semigroups of one-to-one transformations of an infinite set, especially the full semigroup of injective self-maps and the subsemigroup consisting of maps whose defect has the cardinality of the set. It classifies stable equivalences, normal complexes, ideals, and normal subsemigro…
This paper studies boundary value problems for linear and quasilinear parabolic equations in a cylinder, focusing on generalized solutions under weak coefficient assumptions and natural growth conditions. Using integral inequalities for level sets and De Giorgi type iteration arguments, the authors …
This paper studies expansion of functions in quasi-power series on the nonfundamental interval t greater than u, contrasting this problem with earlier results for the interval (0,u]. It introduces a smoothness class defined through iterated differential operators associated with a nondecreasing sequ…
This paper addresses the computation of the topological index of an isolated fixed point of a completely continuous vector field when the linearization is degenerate. It develops an algorithm that reduces the problem to the rotation of an induced finite-dimensional field on a sphere, after transform…
This note studies smoothness properties of generalized potentials associated with a second-order elliptic operator in a bounded domain with an interior separating surface. It formulates transmission boundary-value problems for simple-layer, double-layer, and volume potentials, and proves existence, …
This note studies estimation of the spectral distribution function of a real stationary Gaussian process from a finite discrete-time sample, focusing on the integrated periodogram estimator and its convergence properties. It shows that although the Lévy distance between the estimator and the true sp…
The paper derives quantitative estimates for real algebraic hypersurfaces and for derivatives of rational functions in real and complex variables. Using an integral-geometric lemma relating hypersurface measure to intersections with lines, it bounds the size of epsilon-nets, neighborhood volumes, an…
The paper studies discrete random sequences whose means and covariance functions are periodic in time, and characterizes when a proposed periodic covariance representation can arise from such a sequence. By reducing the problem to the correlation matrix of a finite-dimensional stationary sequence, i…
The paper studies continuity criteria for Nemytskii operators generated by functions measurable in the independent variable and continuous in the dependent variables, acting between Orlicz spaces in the Zaanen, Luxemburg formulation. It first gives necessary and sufficient growth conditions for such…
This note studies boundary-value problems on the whole real line for a special second-order nonlinear differential equation with limiting conditions at negative and positive infinity, and for an analogous autonomous third-order equation. For the second-order problem, it establishes existence under g…
This paper studies quadrature formulas for multidimensional integration over the unit cube using deterministic point nets, measured by a dyadic nonuniformity quantity that controls the error for functions in the Hölder-type class \(H_\alpha\). It defines this measure through irregularities of dyadic…
This paper develops convergence and divergence tests for multiple series with positive terms, extending root and ratio type criteria along rays in the positive orthant. It introduces a condensation procedure for multiple series and proves, under positivity, continuity, and monotonicity assumptions, …
The paper studies functions of several variables with different differentiability orders and integrability exponents in different coordinate directions, using anisotropic spaces defined through directional derivatives and finite differences. Starting from an integral identity for mixed derivatives o…
The paper constructs finite integral Hankel transforms from expansions in eigenfunctions of a Sturm-Liouville problem whose differential equation is Bessel’s equation on a finite interval with third-kind boundary conditions. It derives the eigenfunctions, characteristic equation, normalization, and …
This paper completes the regularity theory for convex surfaces in Euclidean space whose intrinsic metric is sufficiently regular and has positive Gaussian curvature. Building on the author’s earlier result for metrics of class at least C5, the argument uses analytic approximation by convex caps, Hei…
The paper introduces the notion of a continual basis in a separable Hilbert space, formulated as a linear mapping into measurable functions with a unique integral representation of each inner product. It defines conjugate, integrally bounded, orthogonal, Bessel, Hilbertian, and Fischer-Riesz mapping…
This paper studies extremal norms of linear operators on continuous functions on the interval [-1,1] that reproduce the kth derivative on algebraic polynomials of degree at most n, comparing general operators with operators whose values are polynomials of degree at most n. It proves that in the nonp…
This paper studies the Green function for a second order uniformly parabolic equation in a bounded domain with a sufficiently regular boundary and Robin type boundary condition. Under weak regularity assumptions on the coefficients and boundary data, it records representation of solutions by the Gre…
The paper develops an analogue of Schmidt’s reduction method for a nonlinear integral equation arising from the Dirichlet problem for the equation with quadratic nonlinearity in a bounded planar domain. Using Green’s formula and weighted a priori estimates, it obtains bounds for all possible solutio…
This note establishes estimates for the analytic capacity of bounded closed plane sets, using approximation by rational functions with poles off the set and the relation between analytic capacity and the quantity \(p_F(1)\) when the boundary length parameter is finite. The authors derive comparison …
This note studies discontinuous variational problems in an \((n+1)\)-dimensional space, where the integrand has a first-kind discontinuity across an intermediate manifold and admissible curves have movable endpoints and a corner on that manifold. It formulates the minimization problem for a broken c…
The paper proves that the elementary theory of the class of all finite groups is undecidable, addressing a problem noted by Tarski, Mostowski, and Robinson. The argument first constructs, for finite-dimensional algebras over an arbitrary fixed field, first-order formulas that represent any normally …
The note proves a limit theorem for normalized sums of independent random variables whose densities may take nonpositive values and whose moments vanish up to order \(2q-1\), with a prescribed \(2q\)-th moment. Under analogues of bounded variance and Lindeberg conditions, together with an additional…
The paper proves a Phragmén-Lindelöf type principle for solutions of first-order linear elliptic systems with constant matrix coefficients in a half-strip. For systems whose principal matrix has eigenvalues with nonzero imaginary parts, it assumes controlled Hölder behavior and growth on the two hor…
This note extends Linnik-type results on the least prime in an arithmetic progression to prime ideals in algebraic number fields and to primes represented by primitive binary quadratic forms. Using zero-free regions and zero-density estimates for Hecke zeta functions, together with contour integrati…
This paper studies whether a closed regular convex surface of positive Gaussian curvature, after removal of finitely many points, can admit nontrivial isometric transformations within the class of regular surfaces. Focusing on the case of two punctures, it constructs auxiliary Riemannian and locally…
The paper studies tame and normal embeddings of triangulable manifolds and elements in Euclidean spaces, with emphasis on when normality implies tameness. Using consequences of Brown’s results on cellular sets and spheres, it proves a necessary and sufficient criterion for a tame embedding of a k-di…
The paper studies linear systems of ordinary differential equations with general two point boundary conditions and proposes reducing them to a sequence of simpler boundary value problems in which prescribed components are split between the endpoints, including the Cauchy problem as a special case. I…
This paper studies first boundary-value problems for certain quasilinear parabolic systems whose first-order coefficients may grow rapidly in the unknown functions. It derives an a priori integral estimate by introducing a convex solution of an associated second-order equation in the variables of th…
The paper studies the non-self-adjoint half-line differential operator defined by a complex boundary condition and a continuous potential, focusing on the structure of its discrete spectrum and singular, or exceptional, points on the continuous spectrum. It gives criteria, based on moment and quasi-…
This paper classifies integral indecomposable representations of the four-group generated by two commuting involutions, equivalently pairs of commuting integral unimodular matrices whose squares are the identity. The argument separates a natural sublattice on which the two generators agree, reduces …
This paper develops a priori estimates in fractional and anisotropic Sobolev type spaces for several elliptic and parabolic boundary value problems. It introduces and compares function spaces defined through directional difference and derivative norms, proves trace and extension results including ex…
This note proves a uniqueness theorem for an inverse problem of the metaharmonic volume potential for bounded simply connected bodies of equal constant density in three-dimensional space. Using methods from earlier work on inverse potential problems, it considers two piecewise smooth bodies whose ex…
This note defines characteristic classes for complex representations of finite groups by applying Chern classes to the vector bundle over the Eilenberg-MacLane space associated with a representation. The construction is formulated as a natural transformation from the representation ring, viewed as a…
This note proves a Phragmen-Lindelof type uniqueness theorem for harmonic functions in a rectangular cylinder with zero boundary values, bounded normal derivative on two opposite faces, and prescribed double exponential growth in the axial variable. The proof expands the function in sine eigenfuncti…
This note studies the second order differential operator on the half-line defined by \(-y''+q(x)y\) with a separated boundary condition at the origin, focusing on sufficient conditions under which the operator is not self-adjoint and has deficiency indices \((1,1)\). It derives an a priori estimate …
This note extends the length and area principle from analytic functions to non-univalent Q-quasiconformal interior mappings of arbitrary plane domains. It formulates an integral inequality relating the total spherical length of level curves of the mapping, the average multiplicity of preimages, and …
The paper studies effective solution methods for singular Tricomi problems associated with the Chaplygin equation arising in transonic flow theory. It constructs Duhamel type Riemann resolvents for the first and second singular Tricomi boundary value problems by transforming the equation, expanding …
This paper studies the representation of solutions of homogeneous partial differential equations with constant coefficients as Fourier transforms of functionals supported on the zero set of the defining polynomial. It formulates and proves, for several spaces of entire functions, generalized functio…
This paper studies eigenfunction problems for a second order linear self-adjoint elliptic operator whose coefficients are discontinuous across an interior surface, with continuity of the function and conormal derivative imposed at the interface. Under regularity, ellipticity, and nonnegativity assum…
This paper studies an integral geometry problem in three-dimensional complex affine space: reconstructing a sufficiently regular rapidly decreasing function from its integrals over the lines of an algebraic complex. The authors formulate a tangency condition on the complex, give an equivalent differ…
This note extends Pontryagin’s maximum principle to optimal control problems for systems whose state equations contain a fixed delay in the phase variables but not in the controls. The problem is formulated with a prescribed initial history, a terminal manifold condition, free terminal time, and an …
This paper studies the Cauchy problem for higher order normal hyperbolic equations with periodic spatial variables and variable coefficients. It constructs explicit and implicit finite difference schemes and proves their stability through discrete energy estimates based on a difference analogue of t…
This paper studies iterative methods with minimal residuals for solving nonlinear operator equations in a real Hilbert space. Starting from a general iteration with a scalar step chosen to minimize the norm of the linearized residual, it derives two principal schemes, one using the current residual …
The paper studies Borel-type interpolation in non-quasianalytic classes of infinitely differentiable functions whose derivatives satisfy bounds of the form \(B^n n^{n\beta}\), with \(\beta>1\). Using estimates for Fourier transforms of functionals concentrated at a point, refined Phragmen-Lindelof a…
